본문 바로가기
KERD
논문KCI 등재

On the measure of non strict cosingularity and the theory of operator matrix

Ines Walha|Naila Bouida
대한수학회 (The Korean Mathematical Society)|2024.10|대한수학회논문집 (Communications of the KMS)|제39권 제4호|pp. 875-895|DOI 10.4134/CKMS.c230344

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Measure of non strict cosingularitytheory of Fredholm operatorsoperators theorytheory of operator matricesessential spectra
주제분류수학

초록

Measure of non strict cosingularity appears as one of the most particular class of Fredholm perturbation allowing to draft an interesting use in the analysis of spectral properties of linear operators in particular operator matrix field. The main purpose of this paper is to establish some new stability results of perturbed lower semi-Fredholm (semi-Weyl) operators linked to the use of measure of non strict cosingularity and the theory of Fredholm inverse. Moreover, we apply our results in order to investigate a new framework of the characterization of some essential spectra of unbounded block $3\times 3$ operator matrix with maximal domain.

Abstract

Measure of non strict cosingularity appears as one of the most particular class of Fredholm perturbation allowing to draft an interesting use in the analysis of spectral properties of linear operators in particular operator matrix field. The main purpose of this paper is to establish some new stability results of perturbed lower semi-Fredholm (semi-Weyl) operators linked to the use of measure of non strict cosingularity and the theory of Fredholm inverse. Moreover, we apply our results in order to investigate a new framework of the characterization of some essential spectra of unbounded block $3\times 3$ operator matrix with maximal domain.

참고문헌 (30)

  1. F. Abdmouleh, "Spectral description of Fredholm operators via polynomially Riesz operators perturbation", Georgian Math. J, 29(3), pp.317~333 (2022)[DOI]
  2. A. Bahloul, "Generalized Drazin invertibility of operator matrices", Numer. Funct. Anal. Optim, 43(16), pp.1836~1847 (2022)[DOI]
  3. A. B´atkai, "Spectral problems for operator matrices", Math. Nachr, 278(12-13), pp.1408~1429 (2005)[DOI]
  4. S. Bouzidi, "On the criteria of a measure of non strict cosingularity in the description of spectral properties of operator matrix", Georgian Math. J (2024)[DOI]
  5. J. A. Burns, "Distributed Parameter Systems", pp.23~39 (1987), Springer-Verlag
  6. J. A. Burns, "Feedback control of a hyperbolic partial-differential equation with viscoelastic damping", Control Theory Adv. Tech, 5(2), pp.157~188 (1989)
  7. S. Charfi, "On relative essential spectra of block operator matrices and application", Bull. Korean Math. Soc, 53(3), pp.681~698 (2016)[DOI]
  8. R. Cross, "Characterisations of operators of lower semi-Fredholm type in normed linear spaces", Quaestiones Math, 15(2), pp.151~173 (1992)
  9. K. -J. Engel, "Spectral theory and generator property for one-sided coupled operator matrices", Semigroup Forum, 58(2), pp.267~295 (1999)[DOI]
  10. K. -J. Engel, "One-Parameter Semigroups for Linear Evolution Equations" (2000), Springer
  11. A. S. Fa˘ınshte˘ın, "Spectral theory of operators and its applications, No. 6", pp.182~195, “`Elm”, Baku
  12. K. -H. F¨orster, "Semi-Fredholm operators and sequence conditions", Manuscripta Math, 44(1-3), pp.35~44 (1983)[DOI]
  13. Z. Fuzhen, "The Schur Complement and Its Applications" (2005), Springer-Verlag
  14. M. Gonz´alez Ortiz, "Operational quantities derived from the norm and measures of noncompactness", Proc. Roy. Irish Acad. Sect. A, 91(1), pp.63~70 (1991)
  15. A. Majorana, "Space homogeneous solutions of the Boltzmann equation describing electron-phonon interactions in semiconductors", Transport Theory Statist. Phys, 20(4), pp.261~279 (1991)[DOI]
  16. A. Martin´on, "Operational quantities in Fredholm theory (Spanish)", Doctorales, pp.1990
  17. I. Marzouk, "New approach on the study of operator matrix", Georgian Math. J, 31(2), pp.315~330 (2024)[DOI]
  18. A. Matsumura, "The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids", Proc. Japan Acad. Ser. A Math. Sci, 55(9), pp.337~342 (1979)
  19. M. Mokhtar-Kharroubi, "Mathematical Topics in Neutron Transport Theory" (1997), World Sci. Publishing, Inc
  20. V. M¨uller, "Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, Operator Theory: Advances and Applications", pp.139~ (2003), Birkh¨auser Verlag
  21. R. Nagel, "Well-posedness and positivity for systems of linear evolution equations", Confer. Sem. Mat. Univ. Bari, (203), pp.29~ (1985)
  22. R. Nagel, "Characteristic equations for the spectrum of generators", Ann. Scuola Norm. Sup. Pisa Cl. Sci, 24(4), pp.703~717 (1997)
  23. M. Z. Nashed, "Proceedings of an Advanced Seminar Sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, October 8–10, 1973 (No. 32)" (2014), Elsevier
  24. V. Rakoˇcevi´c, "Measures of non-strict-singularity of operators", Mat. Vesnik, 35(1), pp.79~82 (1983)
  25. M. Schechter, "Principles of Functional Analysis" (2002), Amer. Math. Soc
  26. C. Tretter, "Spectral Theory of Block Operator Matrices and Applications" (2008), Imp. Coll. Press
  27. I. Walha, "On the M-essential spectra of two-group transport equations", Math. Methods Appl. Sci, 37(14), pp.2135~2149 (2014)[DOI]
  28. L. Weis, "¨ Uber strikt singul¨are und strikt cosingul¨are Operatoren in Banachr¨aumen", pp.1974
  29. S. ˇC. ˇZivkovi´c-Zlatanovi´c, "Measures of non-strict-singularity and non-strict-cosin gularity", Mat. Vesnik, 54(1-2), pp.1~7 (2002)
  30. S. ˇC. ˇZivkovi´c-Zlatanovi´c, "Some geometric characteristics and perturbations of semi-Fredholm operators", Filomat, 30(11), pp.2869~2891 (2016)[DOI]

관련 논문AI추천

On left-right generalized Fredholm spectra and some perturbations resultsAbdelhalim Azzouz, Bilel Krichen, Mahamed Beghdadi대한수학회 · 대한수학회보2025 · 제62권 제6호Some Fredholm theory results around relative demicompactness conceptAref Jeribi, Bilel Krichen, Wajdi Chaker대한수학회 · 대한수학회논문집2021 · 제36권 제2호SPECTRAL PROPERTIES OF THE SUM OF TWO OPERATORS MATRICES VIA RELATIVELY FREDHOLMNESS PERTURBATIONSSana Bouzidi대한수학회 · 대한수학회논문집2024 · 제39권 제4호Shechter spectra and relatively demicompact linear relationsAref Jeribi, Aymen Ammar, Slim Fakhfakh대한수학회 · 대한수학회논문집2020 · 제35권 제2호Property $(\omega)$ for 2-by-2 upper-triangular operator matricesGaohuizi Feng, Pengtong Li대한수학회 · 대한수학회보2025 · 제62권 제4호On weighted and pseudo-weighted spectra of bounded operatorsGhazi Kacem, Hatem Baloudi, Nassim Athmouni대한수학회 · 대한수학회논문집2018 · 제33권 제3호

이 간행물의 다른 논문 (15건)

On graded radical ideals of graded non-commutative ringsNico Groenewald, Susan F. EL-Dekenpp. 821-837Antinormal operators and antinormality of composition operators on $L^2(X)$Harish Chandra, Arvind Bhattpp. 839-849COEFFICIENT BOUNDS USING FABER POLYNOMIAL FOR A NEW SUBCLASS OF MEROMORPHIC BI-UNIVALENT FUNCTIONSThambidurai Janani, Sibel Yalcinpp. 851-858Sharp bounds for the initial coefficients for certain families of bi-univalent functionsAhmad Motamednezhad, Safa Salehianpp. 859-873SPECTRAL PROPERTIES OF THE SUM OF TWO OPERATORS MATRICES VIA RELATIVELY FREDHOLMNESS PERTURBATIONSSana Bouzidipp. 897-915
원문 보기